1549301742-The_Theory_of_Difference_Schemes__Samarskii

(^296) Difference Schemes for Elliptic Equations with x 1 = h;/12 and x 2 = h;/12 incorporated. The operators A 1 and A 2 are se ...

Higher-accuracy sche1nes for Poisson's equation 297 it being understood that for any steps h 1 and h 2 the solution of problem ( ...

298 Difference Schemes for Elliptic Equations These properties are an immediate implication of the chain of the relations For p ...

Difference Schemes for Time-Dependent Equations with Constant Coefficients In this chapter difference schemes for the simplest t ...

300 Difference Schernes with Constant Coefficients The original problem. The heat diffusion process on a straight line is descr ...

Heat conduction equation with constant coefficients 301 The family of six-point schemes. As before, it will be convenient to in ...

302 Difference Sche1nes with Constant Coefficients The boundary and initial conditions (5) and (6) are specified at the boundary ...

Heat conduction equation with constant coefficients 303 The six-point symmetric scheme with (} = 0.5 ascribed to Crank and Nicol ...

304 Difference Schernes with Constant Coefficients is the error of approxin1ation (residual) for scheme (II) on the solution 11 ...

Heat conduction equation with constant coefficients 305 yields (12) h^2 2 4 2 y0 = ( L u - ll + <p) + ( O" - 0. 5) T L 1l ...

306 Difference Schemes with Constant Coefficients Stability with respect to the initial data. Let us investigate the stability ...

Heat conduction equation with constant coefficients 307 To decide for yourself whether scheme (16) is stable with respect to the ...

308 Difference Schemes with Constant Coefficients The eigenfunctions { X (k)} constitute an orthonormal system for which Parseva ...

Heat conduction equation with constant coefficients 309 and the harmonic in question is stable. Under the choice I qk I < 1, ...

310 Difference Schemes with Constant Coefficients Under the constraint (} > () 0 it is not difficult to verify that m:;x I qk ...

Heat conduction equation with constant coefficients 311 So, not only the order of approximation, but also the stability of schem ...

312 Difference Schemes with Constant Coefficients Putting these together with (26) we find that N-l N-l N-1 fJ = L T',, x (k) = ...

Heat conduction equation with constant coefficients 313 implying that 1 + O"L\ > E for all k = 1, 2, ... , N - 1 and providin ...

314 Difference Schemes with Constant Coefficients This type of situation is covered by the following assertion. If scheme (II) i ...

Heat conduction equation with constant coefficients or cry Yi-1 - (2 err+ 1) Yi+ cry Y;+1 =-Fi, i = 1, 2, ... , N - 1, (37) Fi= ...